Solving Basic Equations Worksheets - Free Printable

Problem: Solve the following equations using inverse operations. Show your work.

#### Equations:
1. \( \frac{Y}{1} + 3 = 13 \)
2. \( 3 + \frac{Y}{1} = 13 \)
3. \( 9 + \frac{Y}{8} = 10 \)
4. \( \frac{Y}{9} + 3 = 4.1 \)
5. \( 9 + \frac{4}{Y} + 4^2 = 25.4 \)
6. \( 7 + \frac{Y}{1} = 16 \)
7. \( 1 + \frac{Y}{8} = 1.1 \)
8. \( \frac{Y}{9} + 5 = 5.6 \)
9. \( 4 + \frac{Y}{1} = 8 \)
10. \( \frac{Y}{3} + 8 = 10 \)

---

Solution:

#### 1. \( \frac{Y}{1} + 3 = 13 \)
- Simplify \( \frac{Y}{1} \) to \( Y \):
\[
Y + 3 = 13
\]
- Subtract 3 from both sides:
\[
Y = 13 - 3
\]
\[
Y = 10
\]

#### 2. \( 3 + \frac{Y}{1} = 13 \)
- Simplify \( \frac{Y}{1} \) to \( Y \):
\[
3 + Y = 13
\]
- Subtract 3 from both sides:
\[
Y = 13 - 3
\]
\[
Y = 10
\]

#### 3. \( 9 + \frac{Y}{8} = 10 \)
- Subtract 9 from both sides:
\[
\frac{Y}{8} = 10 - 9
\]
\[
\frac{Y}{8} = 1
\]
- Multiply both sides by 8:
\[
Y = 1 \times 8
\]
\[
Y = 8
\]

#### 4. \( \frac{Y}{9} + 3 = 4.1 \)
- Subtract 3 from both sides:
\[
\frac{Y}{9} = 4.1 - 3
\]
\[
\frac{Y}{9} = 1.1
\]
- Multiply both sides by 9:
\[
Y = 1.1 \times 9
\]
\[
Y = 9.9
\]

#### 5. \( 9 + \frac{4}{Y} + 4^2 = 25.4 \)
- Simplify \( 4^2 \):
\[
9 + \frac{4}{Y} + 16 = 25.4
\]
- Combine constants on the left side:
\[
25 + \frac{4}{Y} = 25.4
\]
- Subtract 25 from both sides:
\[
\frac{4}{Y} = 25.4 - 25
\]
\[
\frac{4}{Y} = 0.4
\]
- Take the reciprocal of both sides and solve for \( Y \):
\[
Y = \frac{4}{0.4}
\]
\[
Y = 10
\]

#### 6. \( 7 + \frac{Y}{1} = 16 \)
- Simplify \( \frac{Y}{1} \) to \( Y \):
\[
7 + Y = 16
\]
- Subtract 7 from both sides:
\[
Y = 16 - 7
\]
\[
Y = 9
\]

#### 7. \( 1 + \frac{Y}{8} = 1.1 \)
- Subtract 1 from both sides:
\[
\frac{Y}{8} = 1.1 - 1
\]
\[
\frac{Y}{8} = 0.1
\]
- Multiply both sides by 8:
\[
Y = 0.1 \times 8
\]
\[
Y = 0.8
\]

#### 8. \( \frac{Y}{9} + 5 = 5.6 \)
- Subtract 5 from both sides:
\[
\frac{Y}{9} = 5.6 - 5
\]
\[
\frac{Y}{9} = 0.6
\]
- Multiply both sides by 9:
\[
Y = 0.6 \times 9
\]
\[
Y = 5.4
\]

#### 9. \( 4 + \frac{Y}{1} = 8 \)
- Simplify \( \frac{Y}{1} \) to \( Y \):
\[
4 + Y = 8
\]
- Subtract 4 from both sides:
\[
Y = 8 - 4
\]
\[
Y = 4
\]

#### 10. \( \frac{Y}{3} + 8 = 10 \)
- Subtract 8 from both sides:
\[
\frac{Y}{3} = 10 - 8
\]
\[
\frac{Y}{3} = 2
\]
- Multiply both sides by 3:
\[
Y = 2 \times 3
\]
\[
Y = 6
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ Y = 10 \\
2. & \ Y = 10 \\
3. & \ Y = 8 \\
4. & \ Y = 9.9 \\
5. & \ Y = 10 \\
6. & \ Y = 9 \\
7. & \ Y = 0.8 \\
8. & \ Y = 5.4 \\
9. & \ Y = 4 \\
10. & \ Y = 6 \\
\end{aligned}
}
\]